Geoinformatics 2021 11-14 May 2021, Kyiv, Ukraine

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Neural network modeling in the problem of localizing the sources of seismic events in the territory of Ukraine in order to assess the seismic risk zones of industrialized territories.

*O. Herasymenko (Institute of Geophysics of the National Academy of Sciences of Ukraine), А. Kendzera (Institute of Geophysics of the National Academy of Sciences of Ukraine), L. Shumlianska (Institute of Geophysics of the National Academy of Sciences of Ukraine), A. Ganiev (Institute of Geophysics of the National Academy of Sciences of Ukraine), K. Petrenko (Institute of Geophysics of the National Academy of Sciences of Ukraine), N. Ostapchuk (Institute of Geophysics of the National Academy of Sciences of Ukraine)

SUMMARY

In order to identify areas of seismic risk in industrial regions of Ukraine, the authors used the possibilities of neural network modeling in the problem of localizing earthquake sources, registered, according to monitoring data 2007-2020, by a network of seismic stations IGF NASU "Odessa", "Skvira", "Poltava", "Nikolaev". Local hodographs of P-, S - earthquake waves of the Ukrainian shield and the Dnieper-Donetsk depression in the range of magnitudes 2.7-4.8 were constructed. Modeling localization problems in the operational mode allows to construct with sufficient accuracy the sources of seismic events in the territory of Ukraine, which is confirmed by the examination of the results obtained by global travel time curves D-B. Examples of localization of earthquakes of 2011, 2013 with magnitudes 3.9 and 4.6 in the Krivoy Rog basin area provide additional opportunities for analyzing the structural features of the lithosphere, and in the future – real-time evaluation of the characteristics of the seismic process in the task of its prevention.

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Introduction. Historically, the idea of a real threat of earthquakes in the territory of Ukraine from a deep-focus source in the Vrancea region has been formed. Therefore, the seismic monitoring of the territory of Ukraine of three autonomous digital seismic stations of the new generation NARS "Skvira", "Odessa", "Poltava", since 1997, was focused on this high-risk object. However, with the advent of the new millennium, an important problem of the seismological service of Ukraine has become the construction of local travel time curves in the problem of localizing earthquakes in the territory of Ukraine due to an increase in the magnitude of local earthquakes, exceeding the level of the noise threshold. The consequences of the activities of industrially developed regions of Ukraine led to interference in the structure of the lithosphere - disruption of the geodynamic equilibrium of the suture zones of the Ukrainian shield and displacement of the seismic boundaries of the Dnieper-Donetsk avlocagen, and, as a consequence, local earthquakes of 1996-97 and activation of local events of 2007-2019 in the range of magnitudes 3.0-4.8. The configuration of the location of the IGF seismic stations, supplemented by the s/s "Mykolaev", "Dnipro", "Kremenchug" since 2010, is aimed at studying 1) the patterns of distribution of the intensity of earthquakes in Vrancea earthquakes in the territory of Ukraine and 2) the peculiarities of inter - and intraplate seismic activity of tectonic structures of central regions of the country.

Methods of investigation. Under the guidance of the supervisor Ph.D., S.Sc. Lazarenko according to the monitoring data of 2001-2016, the formation of a digital database of seismological information for the construction of regional and local multi-parametric hodographs based on earthquake registration data of Ukraine and abroad was initiated. To solve the problem in the theoretical aspect of Lazarenko developed programs using the mathematical apparatus of the MS Develop Visual Studio DVF environment for multilayer, fully connected, direct-flow, controlled networks of artificial neurons, in which learning is carried out by the method of error feedback (Lazarenko and Gerasimenko, 2010; Lazarenko et al., 2011). The functioning of the neural network consists of the following stages: a) the organization of the training set, b) the actual training and c) the operating mode - the examination of the network with the help of a training sample that did not participate in training. The event recorded at the seismic station is characterized by a five-dimensional vector of parameters with components: depth of focus of the earthquake, magnitude, reverse azimuth, epicentral distance, travel time of longitudinal and transverse waves:

nnnnin txxxx ,,,, 4,2,1,,

where hx 1 (hypocenter depth), Mx 2 (magnitude), rx 3 (distance), azbx _4 (reverse

azimuth), nt is a target value equal to the time of arrival to the observation point of a certain phase of

the wave excited by the n-th earthquake. Formation of the training set in the problem of construction of neural network models of local hodographs of P- and S-waves was selected the most conditional seismological information at epicentral distances ≤ 10°, depth ≤ 50 km, from 259 three-component earthquake records, respectively at stations: "Skvira" -72 "-123," Poltava "-38," Nikolaev "-26. IGF seismic stations registered 42 local seismic events, including dangerous within industrial areas events of densely populated areas with a magnitude in the range of 3.7-4.8, of which - 25/12/07, 11/01/14, 23/06/13 ( Kr.Rog, mb = 3.7, 3.9, 4.6), 03/02/15 (Sumy, mb = 4.6), 19/07/15 (Tyachev, Zakarpattia, mb = 3.9), 18/10/15 (Sea of Azov, mb = 4.7), 07/08/16 (Mariupol, mb = 4.8), 30/05/19 (Mykolaiv, mb = 4.1), as well as 27 earthquakes with magnitude <3.5. To build a training sample of neural network models of P- and S-wave hodographs, the coordinates, time and depth of earthquakes were selected from the most conditional seismological information of international centers NEIC, EMSC, NCCA NSAU, Carpathian and Crimean network stations, GS RAS (OBN). When interpreting low-energy signals, a major obstacle to the separation of the entry of seismic signals is the noise of the tracks, which leads to additional errors of interpretation, as well as the noise absorption of the phases of local earthquakes. The use of many parametric neural network models of the hodograph allows the best way to average the noisy observational data linking two quantities: wave travel time and distance. In-depth analysis of seismic records by means of MS-DOS PITSA

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programmable application packages (Programmable Interactive Toolbox for Seismological Analysis) (Sherbaum, et al 1994), , makes it possible to qualitatively distinguish the time of entry of substandard material. Examples of interpretation of the Z-component of the registered P-, S-waves of local seismic events with the clearest phases of seismic entry are presented in Figure 1a and Figure 1b - samples of typical registrations. The parameters of the earthquakes are presented via the EMSC Internet service.

Figure 1 Areas of registration of the Z-component of local earthquake recording: a) 14.01.2011, φ = 48.14º, λ = 33.29º, M = 3.9, h = 30km, registered with s / s "Poltava", Δ = 187km, "Skvira", Δ = 319km; b) 03.01.2013, φ = 47.01º, λ = 25.36º M = 3.4, h = 5km, s / s “Poltava”, «= 739km,“ Odessa ”Δ = 424km,“ Skvira ”Δ = 438km

For the whole set of vectors with the help of the selected educational structure a matrix of codes was formed, which has the ability to generalize the original set and thus predict the behavior of the system being modeled, or its individual elements. The iterative learning procedure was conducted with the teacher, at the output of the network the target function was set - the deviation from which for each of the vectors of the learning set of a separate station after the end of the learning process must be minimal. In our example, such a target value is the travel time of two phases - the entry of waves P and S, registered at the stations of the observation network. Learning the network for each signal (input vector) occurs in two stages: a) direct propagation less the root mean square error, which determines the level of learning of the network:

m

jjj ytE

1

22/1

where for the j-th node - the target value, the running output, and b) the reverse transmission of the error, which minimizes the error of the network by the method of the fastest descent, thus adjusting the weight of the neurons

ijijij d

dEttw

)()1(

where is the weight of the connection between the i-th node of the layer l and the j-th node of the layer l-1, t is the iteration number, μ is the coefficient of learning speed. The learning process is considered to have coincided when the error price reaches a given value, or does not change for a sufficient number of iterations. Network training begins with a gradient descent from some point on the surface of the error function, which is determined by many random initiating (starting) values of weights, trying to reach its global minimum, which will determine the end of the iterative learning process. Thus, a set is formed for training a network of artificial neurons, which (after training) will form a model of time registration of the phases of seismic waves of an individual seismic station. The network architecture was selected by trial and error, and the best, given the rate of convergence of the iterative learning process and the magnitude of the final error, were the structures of a single-layer network with architecture NM = 4: 10: 1 on records s/s "Skvira", s/s Odessa ", and two-layer – s/s" Poltava", NN = 4: 4: 5: 1 and s/s" Nikolaev", NN = 4: 10: 5: 1 The conducted test of various combinations of number of knots and coefficients of speed of training showed that the optimal range for the speed of convergence of the learning process and the smoothness of the error function is

10.120.2 EE for single-layer and 10.520.1 EE for two-layer models (Figure 2).

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The model obtained in the operational mode is able to form nonlinear models of the time propagation field of seismic wave phases of the studied region as a function of several arguments, in our case: source depth, magnitude, wave arrival azimuth and epicentral distance.

Figure 2 Behavior of the loss function depending on the number of iterations in the training of neural models of P, S-waves registered by the seismic stations of the IGF of NASU

Including the time of registration of the seismic wave at the registration station, excited at any point in the study region, with the source parameters that lie within the intervals of existence of the constituent vectors of the training sample. The matrix of codes, obtained as a result of the network in the learning mode, was used in the operational mode: neural network, it was proposed to determine the travel time of the phase of the wave generated by the vector, with the coordinates:

1000.1,~,/)_(~,/)(~,/)(~4321 kxnazbxnMxnhx k

nh

where n is the number of members of the set of the training sample. From the database registered by seismic stations, 8 events were selected that did not participate in the training, but were stored for the exam. The trained neural network was excited by a signal (parameter vector) formed from the examination sample, and the network output was compared with the desired values in our case tp , ts - target values equal to the time of arrival at the observation station of the phase of the wave excited by the n-th earthquake.

Results of investigations. Figure 3 shows the graphs of the formed neural network hodographs P and S waves of registration stations (Graph 1, Graph 2). The graph ts-tp with the marked points of the value of ts-p earthquakes of the examination sample obtained after the operation of the network in the operational mode is also given (Graph 5). Quite accurate modeling examples demonstrate the ability to summarize the accumulated knowledge and generate accurate outputs of signals that were not involved in the learning process. In order to determine the efficiency of neural network models of P, -S- wave hodographs, according to the data of the studied database, IASP-91 regional hodographs of Jeffries-Bullen PJB (Graph 3, Graph 4) and JDB (Graph 2) - waves for source depth 0 km (Graph 5) were constructed.

Figure 3 Hodographs of P-, S-phases of seismic waves of local seismic events registered with s / s "Odessa", "Skvira": 1.tp , 2.ts - neural network models; 3. tp. 4. ts model of Jeffries-Bullen (h = 0km). The points on hodograph 5 determine the values of ts-p earthquakes in Ukraine

The program of calculations of hodographs included data of neural network models of P- and S-phase hodographs and values of global hodographs for source depth 0 km according to the given parameters of

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registered earthquakes at seismic stations "Skvira", "Odessa". Examples of the above localizations of earthquake foci were performed by calculating the position of the hypocenter by the WSG program using a model of a homogeneous environment (Figure 4).

Figure 4 Example of localization of earthquakes: (a) Kryvyi Rih basin on June 23, 2013 according to the registration of seismic stations "Poltava", "Skvira", "Mykolayiv"; (b) Slobozhanshchyna 03.02.2015 - s / s "Poltava", "Skvira", "Mykolaiv", "Dnipro"

On Figure 5 the epicenters of local earthquakes in Ukraine are formed by: 1). data from international agencies; 2). the results of neural network modeling; 3). Jeffries-Bullen's hodographer; 4). events that were registered at some Ukrainian seismological stations.

Figure 5 Map of local seismicity of the research region according to the monitoring data of s / s "Skvira", "Odessa", "Poltava", "Nikolaev" 2007-2019 events with magnitude in the range 3.4 - 4.9. Triangles mark network stations; circles - epicenters of earthquakes obtained by hodograph calculations: 1. neural network models (white circles), 2. Jeffries-Boulen (dark). Colored circles indicate local events in the catalogs of the agencies GSKSK, EMSC, the Crimean network, GS RAS

Recommendations and conclusions. The presented initial stage of work on localization of earthquake sources by means of neural network modeling testifies that especially important for development of modeling in an estimation of capacity and position of a seismically active layer of local earthquakes of industrial territories is necessity of building of a supervisory network and studying of its possibilities. The accumulation of information on the influence of the inhomogeneity of the earth's crust on the accuracy of determining the coordinates of earthquake sources makes it possible to obtain more accurate data of modern hazardous seismic zones, which is important for further design and operation of public and industrial facilities.

References Lazarenko, M.A. and Gerasimenko, O.A., [2010] Neural network modeling of seismic wave hodographs.

Geophysical Journal, 32, (5), 26-141. (in Russian). Lazarenko, M.A., Gerasimenko, O.A. and Ostapchuk, N.N. [2011] NN Neural network models of local

hodographs of seismic waves. Geophysical Journal, 33, (6), 157-160. (in Russian).